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A007069 First column of spectral array W(sqrt 2).
(Formerly M1329)
5
1, 2, 5, 7, 9, 11, 12, 15, 16, 19, 21, 22, 25, 26, 29, 31, 33, 35, 36, 39, 41, 43, 45, 46, 49, 50, 53, 55, 57, 59, 60, 63, 65, 67, 69, 70, 73, 74, 77, 79, 80, 83, 84, 87, 89, 91, 93, 94, 97, 98, 101, 103, 104, 107, 108, 111, 113, 115, 117, 118, 121, 123, 125, 127, 128, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
A. Fraenkel and C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discrete Mathematics 126 (1994) 137-149.
FORMULA
From Benoit Cloitre, Apr 06 2003: (Start)
Iterated floor function: a(n) = floor(sqrt(2)*floor(sqrt(2)*n)).
a(n) = A001951(A001951(n)).
a(n) = 2*n - 1 - A059648(n). (End)
MATHEMATICA
Table[Floor[Sqrt[2]*Floor[Sqrt[2]*n]], {n, 1, 100}] (* G. C. Greubel, Aug 16 2018 *)
PROG
(PARI) vector(100, n, floor(sqrt(2)*floor(n*sqrt(2)))) \\ G. C. Greubel, Aug 16 2018
(Magma) [Floor(Sqrt(2)*Floor(Sqrt(2)*n)): n in [1..100]]; // G. C. Greubel, Aug 16 2018
(Python)
from math import isqrt
def A007069(n): return isqrt(isqrt(n**2<<1)**2<<1) # Chai Wah Wu, Aug 29 2022
CROSSREFS
Sequence in context: A007300 A256699 A247421 * A182463 A163985 A130773
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Benoit Cloitre, Apr 06 2003
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)